Castle Garden existed as a processing station for immigrants between 1855 and 1890. There is no separate set of records for Castle Garden, as there is for Ellis Island.
Passenger lists for the Castle Garden time period are available on microfilm so if you know a date of arrival or a ship name you can order the microfilm or have NARA do a lookup for you.
Check the complete list of film numbers (NARA or FHC) for ships going to New York after 1820. Find your date (year, month, day if known) and write down the NARA
or Family History Centre film number you need
NARA & FLH Films for New York Passenger Lists
For more help with this time period see Castle Garden:Ships Passenger Lists to New York 1 Aug.1855 - 18 Apr. 1890